We re-examine the design of structurally regular linear-phase (LP) paraunitary filter banks (PUFBs) via a general framework without the LP constraint, and show that by a suitable choice of parameterization, the general regularity theory simplifies significantly under the LP assumption. A new geometric condition for regularity is presented which is essentially equivalent to but simpler than that in Oraintara et al. (2001). A connection between the general-purpose dyadic-based building block and the order-one LP building block used in the GenLOT structure is established.